Tag: Limits and Structures in Graph Theory
Entropy bounds limit perfect matchings in bipartite hypergraphs
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in MathematicsWhat the study found The authors prove an upper bound on the number of A-perfect matchings in uniform bipartite hypergraphs with small maximum codegree. They also derive bounds for related counting problems in Latin squares and regular hypergraphs. Why the authors say this matters The study suggests that these bounds help quantify how many perfect…
Extremal signed complete graphs with K2,2-minor-free negative subgraphs
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in MathematicsWhat the study found The authors characterize the extremal signed complete graphs that achieve the maximum and second maximum index when the negative-edge-induced subgraph is a K2,2-minor-free spanning subgraph of Kn. Why the authors say this matters The abstract says this work addresses an extremum problem for the index of a signed complete graph based…
Edge version of graph inducibility is determined by fractional independence number
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in MathematicsWhat the study found The study shows that the edge version of inducibility for any graph H satisfies ρ(H,m) = Θ(m^α_f(H)), where α_f(H) is the fractional independence number of H. The authors also give additional bounds and conjectures for paths and cycles. Why the authors say this matters The authors indicate that this result shifts…
